Iran is carrying out a campaign of intimidation and smears against the BBC's Persian TV service, watched by millions of people in the Islamic Republic but loathed by the government in Tehran.

In recent incidents, relatives of BBC staff in London have been detained and threatened by Iranian intelligence agents, top presenters targeted by malicious rumours and one employee subjected to an online interrogation in London after a family member in Iran was jailed. Iran is thought to be preparing a documentary film discrediting the channel in the runup to parliamentary elections next month.

Sadeq Saba, the head of BBC Persian, was accused live on air by an unknown caller of raping Pooneh Ghoddoosi, presenter of popular Persian-language talk show Your Turn. Both insist the charge is entirely without foundation but it has since been repeated as fact by leading Iranian government media outlets.

Iran has repeatedly jammed BBC Persian TV since it was founded in 2009. The latest bout of harassment comes against a background of sharply deteriorating relations between the UK and Iranian governments. Last November Britain shut its Tehran embassy after it was stormed by demonstrators in apparent retaliation for sanctions imposed over Iran's nuclear programme. Iran's London embassy was then ordered closed.

Tensions worsened in recent weeks after the closure of Press TV, the English-language Iranian state broadcaster, in London. The UK regulator, Ofcom, revoked its licence for breaching the Communications Act. BBC Persian staff say they believe Tehran wants to stop the channel covering the elections on 2 March.

Anonymous callers or others using names such as the Cyber Army of Allah have accused BBC Persian staff of being drug dealers, converting to Bahaism or Chrstianity – potentially a capital offence in Iran as it is considered to be apostasy – or taking bribes. "We are well trained to cut these people off when they say rude or libellous things," said Ghoddoosi, whose image has been used in pornographic montages posted on the internet. "They use F-words and C-words non-stop."

Saba said: "Even Stalin or other dictators never did what the Iranian regime is doing with this campaign of intimidation against our journalists. Iran has arrested a group of people and forced them to confess that they have worked for BBC Persian. We have not hired anyone in the country and we condemn these brutal actions."

Journalists arrested recently include Marzieh Rasouli and Parastoo Dokouhaki. Friends believe they are under pressure to confess on camera that they have been collaborating with BBC Persian in Iran.

Saba and Ghoddoosi are popular in Iran, despite the profound official hostility to the BBC channel. The channel is considered such a threat that someone has created a website identical in design to that of BBC Persian to spread allegations against BBC employees. The fake site uses an .ir domain name, which requires government permission.

BBC Persian's reporting has challenged government versions of both the domestic political scene and Iran's troubled relationship with the west. Iranian officials often cite BBC Persian's work as evidence of a foreign plot against the clerical regime. Saba says one news programme is watched by 12 million to 15 million people per week.

Tehran was furious with the BBC's extensive coverage of the disputed 2009 presidential election, which gave Mahmoud Ahmadinejad a second term. During the unrest that followed, BBC Persian conducted hundreds of telephone interviews with protesters who described deaths, injuries and arrests by security forces. The BBC's correspondent was expelled. Last year the BBC secured Iranian agreement to deploy a new resident correspondent, but it has never been implemented.

Last month security forces raided the home of a BBC Persian employee's relative in Tehran, searched and confiscated their belongings and transferred the person to Evin prison. Hours later, a man claiming to be the relative's interrogator at Evin contacted the employee in London, seeking information about the BBC in return for the family member's freedom.

"My brother and mother have both been subject to interrogations in the past two years," said a colleague. "My brother's personal belongings, including his computer, were confiscated. They were asked to persuade me to collaborate and gather information from the BBC."

Fifty-two BBC Persian staff complained this week about the corporation's handling of the issue, calling it "scandalous" that Iranian intelligence was able to interrogate a BBC employee in London. Thompson's statement followed. "This issue is wider than the BBC – other international media face similar challenges," he said. "But it is behaviour that all people who believe in free and independent media should be deeply concerned about."

Initially, BBC staff believed it was best to simply ignore the Iranian campaign. "I and others have received death threats," said Ghoddoosi. "They say 'you are a servant of the imperialist English government. We will kill you like dogs and crush your bones.'

"Virtual harassment is tolerable – being called a whore or whatever. We dismissed it by saying silence was the right answer. But when it came to the point of our relatives getting arrested at airports and having their passports confiscated, or Iranian intelligence being so brazen that they interrogated someone on British soil, we finally decided to speak out."

• This article was amended on 7 February 2012. The original referred to Pooneh Ghoddoosi as the "then" presenter of popular Persian-language talk show Your Turn. She is still presenter of the show and the text has been corrected.